Comparative Penning-Trap Tests of Lorentz and CPT Symmetry

TL;DR

This paper reviews Penning trap experiments testing Lorentz and CPT symmetry, highlighting recent measurements that significantly tighten constraints on possible violations in quantum electrodynamics.

Contribution

It provides a comprehensive review of theoretical and experimental efforts in Penning traps, emphasizing new results that improve bounds on Lorentz and CPT violation coefficients.

Findings

Recent measurements of proton and antiproton magnetic moments greatly improve constraints.

Constraints on Lorentz and CPT violation coefficients are enhanced by factors up to 3000.

The work discusses prospects for future tests in Penning trap experiments.

Abstract

The theoretical and experimental prospects for Lorentz- and CPT-violating quantum electrodynamics in Penning traps are reviewed in this work. With the recent reported results for the measurements of magnetic moments for both protons and antiprotons, improvements with factors of up to 3000 for the constraints of various coefficients for Lorentz and CPT violation are obtained.

Equations

$$\delta {\omega }_L^w=2{\tilde{b}}_w^3-2{\tilde{b}}_{F,w}^{33}B,\delta {\omega }_L^{\overline{w}}=-2{\tilde{b}}_w^{\ast 3}+2{\tilde{b}}_{F,w}^{\ast 33}B,$$

Full text

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1 Introduction

Among the most fundamental symmetries of relativity and particle physics are the Lorentz and CPT invariances. However, in recent years it has been suggested that tiny violations of Lorentz and CPT symmetry are possible in a unified theory of gravity and quantum physics such as strings. [1] The comprehensive and relativistic description of such violations is given by the Standard-Model Extension (SME), [2] a general framework constructed from General Relativity and the Standard Model by adding to the action all possible Lorentz-violating terms. Each of such terms is formed as the contraction of Lorentz-violating operator with a corresponding coefficient controlling the size of Lorentz violation. High-precision experiments across a broad range of subfields of physics, including Penning traps, provide striking constraints on the coefficients for Lorentz violation. [3] In the context of minimal SME, with operators of mass dimension restricted to $d\leq 4$, several studies of observables for Lorentz violation in Penning traps have been conducted. [4] The relevant theory of Lorentz-violating electrodynamics with nonminimal operators of mass dimensions up to six was also developed. [5] More recently, this treatment was generalized to include operators of arbitrary mass dimension using gauge field theory. [6] In this work, we further the study of experimental observables for Lorentz violation by comparing different Penning-trap experiments and extract new constraints on various coefficients for Lorentz violation using the recent published results of the magnetic moments from the BASE collaboration. [8, 7]

2 Theory

For a charged Dirac fermion $\psi$ with mass $m$ confined in a Penning trap, the magnetic moment and the related $g$-factor of the particle can be obtained by measuring two frequencies, the Larmor frequency $\nu_{L}=\omega_{L}/2\pi$ and the cylotron frequency $\nu_{c}=\omega_{c}/2\pi$, and determining their ratio $g/2=\nu_{L}/\nu_{c}=\omega_{L}/\omega_{c}$. In an ideal Penning-trap experiment with the magnetic field $\boldsymbol{B}=B\hat{x}_{3}$ lying along the positive $x^{3}$ axis of the apparatus frame, the leading-order contributions from Lorentz violation to $\omega_{c}$ for both fermion and antifermions vanish, while the corrections to $\omega_{L}$ are given by

[TABLE]

where $w=e^{-}$, $p$ for electrons and protons and $\overline{w}=e^{+}$, $\overline{p}$ for positrons and antiprotons. The tilde quantities are defined as a combination of different coefficients for Lorentz violation. [5]

The expressions for the shifts in the anomaly frequencies (1) are valid in the apparatus frame where the direction of the magnetic field is chosen to be in the positive $\hat{x}_{3}$ direction. The results in terms of the constant coefficients in the Sun-centered frame requires a transformation matrix between the two frames, [9] which reveals the dependence of the anomaly frequencies on the sidereal time and the geometric conditions of the experiment.

3 Applications

For a confined proton or antiproton in a Penning trap, the relevant experiment-independent observables to the studies of the magnetic moments are the 18 coefficients for Lorentz violation ${\widetilde{b}}_{p}^{J}$, ${\widetilde{b}}_{p}^{*J}$, ${\widetilde{b}}_{F,p}^{(JK)}$, and ${\widetilde{b}}_{F,p}^{*(JK)}$, where $J,K=X,Y,Z$ in the Sun-centered frame. A comparison of the magnetic moments of protons and antiprotons in different Penning-trap experiments offers an excellent opportunity to constrain various of the 18 coefficients for Lorentz violation listed above. Existing analysis involving the comparison of the magnetic moments of protons from the BASE collaboration at Mainz and of antiprotons from the ATRAP experiment at CERN is given in our previous work. [5] Recently, the sensitivities of the magnetic moments for both protons and antiprotons have been improved by several orders of magnitude by the BASE collaboration at Main and CERN. [8, 7] Here we conduct a similar comparison analysis using the recent published results to extract improved constraints on coefficients for Lorentz violation.

For the magnetic moment of the proton measured at Mainz, the laboratory colatitude is $\chi\simeq 40.0^{\circ}$ and the applied magnetic field $B\simeq 1.9$ T points to local south, which corresponds to the $\hat{x}$ direction in the standard laboratory frame. For the antiproton magnetic moment measurement at CERN, the laboratory colatitude is $\chi^{*}\simeq 43.8^{\circ}$ and the magnetic field $B^{*}\simeq 1.95$ T points $\theta=60.0^{\circ}$ east of local north. The experimental data for both experiments were taken over an extended time period, so we can plausibly average the sidereal variations to be zero, leaving only the constant parts. Together with the numerical values of other quantities reported by both BASE measurements, we obtain the bounds for ${\widetilde{b}}_{p}^{Z}$, ${\widetilde{b}}_{p}^{*Z}$, ${\widetilde{b}}_{F,p}^{(XX)}$, ${\widetilde{b}}_{F,p}^{*(XX)}$, ${\widetilde{b}}_{F,p}^{(YY)}$, ${\widetilde{b}}_{F,p}^{*(YY)}$, ${\widetilde{b}}_{F,p}^{(ZZ)}$, and ${\widetilde{b}}_{F,p}^{*(ZZ)}$, with improvement factors of up to 3000 compared to the previous results. [5]

Note that among the 18 independent observables in Penning-trap experiments a large number of them remain unexplored to date. Performing a study of sidereal variations could in principle provide sensitivities to other components of the tilde coefficients. Such analysis could be possible once the quantum logic readout currently under development at the BASE collaboration becomes feasible. [10]

Acknowledgments

This work was supported in part by the Department of Energy and by the Indiana University Center for Spacetime Symmetries.